construction of a quadtrilateral will be impossible if
\[\overline{0a}\] is bigger than one half, i.e. if all three points are to the right of the midpoint of the segment. the probability that one is to the right is 1/2 and all three to the right would be
\[(\frac{1}{2})^3\]

the same is true for the other three segments, and the probability that each of them is bigger than one half is also 1/8
so the probability of failure is 4 times 1/8 = 1/2 and therefore so is the probability of success.